The Wave Function ψ of the Riemann Zeta Function ζ(0.5+it):
Jason C. Cole
Abstract
Jason C. Cole
Abstract
There is exciting research trying to connect the nontrivial zeros of the Riemann Zeta function to Quantum mechanics as a breakthrough towards proving the 160-year-old Riemann Hypothesis. This research offers a radically new approach. Most research up to this point have focused only on mapping the nontrivial zeros directly to eigenvalues. Those attempts have failed or didn’t yield any new breakthrough. This research takes a radically different approach by focusing on the quantum mechanical properties of the wave graph of Zeta as ζ(0.5+it) and not the nontrivial zeros directly. The conjecture is that the wave forms in the graph of the Riemann Zeta function ζ(0.5+it) is a wave function ψ. It is made of a Complex version of the Parity Operator wave function. The Riemann Zeta function consists of linked Even and Odd Parity Operator wave functions on the critical line. From this new approach, it shows the Complex version of the Parity Operator wave function is Hermitian and it eigenvalues matches the zeros of the Zeta function.
A significance statement is not available in the OpenAlex record.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
There is exciting research trying to connect the nontrivial zeros of the Riemann Zeta function to Quantum mechanics as a breakthrough towards proving the 160-year-old Riemann Hypothesis. This research offers a radically new approach. Most research up to this point have focused only on mapping the nontrivial zeros directly to eigenvalues. Those attempts have failed or didn’t yield any new breakthrough. This research takes a radically different approach by focusing on the quantum mechanical properties of the wave graph of Zeta as ζ(0.5+it) and not the nontrivial zeros directly. The conjecture is that the wave forms in the graph of the Riemann Zeta function ζ(0.5+it) is a wave function ψ. It is made of a Complex version of the Parity Operator wave function. The Riemann Zeta function consists of linked Even and Odd Parity Operator wave functions on the critical line. From this new approach, it shows the Complex version of the Parity Operator wave function is Hermitian and it eigenvalues matches the zeros of the Zeta function.
Key concepts: Riemann zeta function, Riemann hypothesis, Arithmetic zeta function, Mathematics, Wave function, Eigenvalues and eigenvectors, Conjecture, Mathematical physics